[sage-support] Re: Reserved words (Sage + Cython)
Hi Simon, It is very strange. I use Ubuntu 11.10 and my parameters are: hamsin@hamsin-pc:~/bin/sage-5.0.beta4$ lsb_release -a No LSB modules are available. Distributor ID: Ubuntu Description: Ubuntu 11.10 Release: 11.10 Codename: oneiric hamsin@hamsin-pc:~/bin/sage-5.0.beta4$ gcc --version gcc (Ubuntu/Linaro 4.6.1-9ubuntu3) 4.6.1 Copyright (C) 2011 Free Software Foundation, Inc. This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. hamsin@hamsin-pc:~/bin/sage-5.0.beta4$ uname -a Linux hamsin-pc 3.0.0-16-generic #28-Ubuntu SMP Fri Jan 27 17:44:39 UTC 2012 x86_64 x86_64 x86_64 GNU/Linux sage: version() 'Sage Version 4.8, Release Date: 2012-01-20' I have compiled 5.0.beta4 and received the same bug: sage: version() 'Sage Version 5.0.beta4, Release Date: 2012-02-14' sage: load ./Main.sage Compiling ./CFunc.spyx... in c_PC >>> /home/hamsin/bin/sage-5.0.beta4/local/lib/libcsage.so(print_backtrace+0x31)[0x7f017a535ea9] /home/hamsin/bin/sage-5.0.beta4/local/lib/libcsage.so(sigdie+0x14)[0x7f017a535edb] /home/hamsin/bin/sage-5.0.beta4/local/lib/libcsage.so(sage_signal_handler+0x20c)[0x7f017a535b06] /lib/x86_64-linux-gnu/libpthread.so.0(+0x10060)[0x7f0180453060] /home/hamsin/bin/sage-5.0.beta4/local/lib/libreadline.so.6(PC+0x0)[0x7f017be1942a] Unhandled SIGSEGV: A segmentation fault occurred in Sage. This probably occurred because a *compiled* component of Sage has a bug in it and is not properly wrapped with sig_on(), sig_off(). You might want to run Sage under gdb with 'sage -gdb' to debug this. Sage will now terminate. /home/hamsin/bin/sage-5.0.beta4/spkg/bin/sage: line 304: 16967 Segmentation fault sage-ipython "$@" -i Can anyone reproduce the same bug on Ubuntu? Best regards, Oleksandr -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] sage won't compile on Arch Linux i686
Hello: I just began using sage and was very impressed with its capabilities. Unfortunately, almost as soon as I began using it, I found out the latest version won't compile on Arch Linux and some other distros. Details can be found at these links: http://trac.sagemath.org/sage_trac/ticket/11391 and http://mailman.archlinux.org/pipermail/aur-general/2012-February/017571.html Will these issues ever be addressed? I'd love to keep learning and using sage, but don't want to abandon my current flavor of Linux. Thanks, Rob -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: Reserved words (Sage + Cython)
Dear Oleksandr, On 17 Feb., 15:32, Oleksandr Kazymyrov wrote: > Or just run "Main.sage" from a shell (in this case, variable PATH should > has a path to the sage directory, like this one > "PATH=/home/user/bin/sage/:$PATH"). Then I can not reproduce it. I started a Sage shell, and did %%% (sage subshell) linux-sqwp:CythonBad simon$ PATH=/home/simon/SAGE/work/ cython_change/CythonBad/:$PATH SAGE_ROOT=/home/simon/SAGE/sage-5.0.prealpha0 (sage subshell) linux-sqwp:CythonBad simon$ ls CFunc.spyx CSbox.sage Functions.c Main.py Main.sage Sbox.sage SAGE_ROOT=/home/simon/SAGE/sage-5.0.prealpha0 (sage subshell) linux-sqwp:CythonBad simon$ ./Main.sage Compiling ./CFunc.spyx... in c_PC >>> in PC <<< out in_PC PC = 0 (sage subshell) linux-sqwp:CythonBad simon$ cat Functions.c int PC() { printf("in PC\n"); return 0; } % So, it is indeed the "bad" version, but there is no segmentation fault. As you can see, this is with a recent development version of Sage. The machine: simon@linux-sqwp:~> uname -a Linux linux-sqwp.site 3.1.9-1.4-desktop #1 SMP PREEMPT Fri Jan 27 08:55:10 UTC 2012 (efb5ff4) x86_64 x86_64 x86_64 GNU/Linux simon@linux-sqwp:~> cat /etc/issue Welcome to openSUSE 12.1 "Asparagus" - Kernel \r (\l). simon@linux-sqwp:~> gcc --version gcc (SUSE Linux) 4.6.2 Copyright (C) 2011 Free Software Foundation, Inc. This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. Best regards, Simon -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: Simplification Issue Implicates Canonical Form
In some previous incarnation, where Sage used Maxima for things like this, your simplification happened. (%i1) 1/sqrt(5); 1 (%o1) --- sqrt(5) (%i2) sqrt(5)/5; 1 (%o2) --- sqrt(5) Now we use Ginac for basic symbolic stuff. Once in a while we (i.e., Burcin) changes some internal representation, or Ginac does. But in general I think it just goes for positive powers - you may want to read its documentation. In particular, "sqrt" is not a builtin function ("square root (not a GiNaC function, rather an alias for pow(x, numeric(1, 2)))"), so the behavior is analogous to sage: 1/5^(1/3) 1/5*5^(2/3) Naturally, GiNaC is Not a CAS, so perhaps that is one reason for the distinction. You are also right about black arts! So I don't pretend to judge Maxima *or* Ginac on this one. I'm sorry if that doesn't help, but it might give you some background, at least. - kcrisman -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Simplification Issue Implicates Canonical Form
Hello sage-support, I'm a Sage newbie who just joined the group. Before I get to the meat of my post, I'd like to thank the open source math software community for all of your hard work! Nothing I say should be misinterpreted as a complaint. I have only admiration and gratitude. I ran into an issue that I thought was worth reporting. As I worked on a relatively simple math problem, I noticed that my screen became filled with complicated expressions involving square roots of small integers. I knew the result couldn't be as complicated as it looked. Trying the various simplify methods didn't help. I scratched my head for a while and experimented. I eventually isolated the issue to the fact that Sage doesn't simplify "sqrt(5) / 5" to "1 / sqrt(5)". Worse, it dutifully replaces "1 / sqrt(5)" with "sqrt(5) / 5", implying that an underlying canonical form definition is systematically making expressions more complicated than necessary. I can imagine a theoretical argument about positive exponents being "simpler" than negative exponents of the same magnitude but that argument falls apart quickly in practice. The problem with keeping expressions like "sqrt(5) / 5" is that they grow uncontrollably with subsequent operations. For example, it keeps expressions like "-1/5*(sqrt(-2*sqrt(5) + 5) - sqrt(5))*sqrt(5)" from simplifying to "- sqrt(-2/sqrt(5) + 1) + 1". Several operations later, a screenful of unnecessary radicals completely obscures the underlying math. Given how common square roots of small integers are, particularly in newbie math problems, I expect this issue to be a significant stumbling block for many folks trying to learn Sage. I know that expression simplification is a black art so I can't pretend to know how to fix this issue. However, I'm certain that "1 / sqrt(5)" is simpler than "sqrt(5) / 5" in some important way. For what it's worth, I think that most of us would make that substitution if we were doing math without automated support. -Mark -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: Reserved words (Sage + Cython)
Dear Simon, >> But the only difference between the good and the bad version is that some function is called PC in the bad file and PCc in the good file Yes, exactly. >> However, Oleksandr: What is one supposed to do in order to reproduce the error? When I start a sage session and attach Main.sage, then it fails with both the bad and the good version. You should replace: if __name__ == "__main__": sys.exit(main()) by main() Or just run "Main.sage" from a shell (in this case, variable PATH should has a path to the sage directory, like this one "PATH=/home/user/bin/sage/:$PATH"). Best regards, Oleksandr -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: How-to change the size of ticks ? ( use of graphs for presentations )
On 2/17/12 7:40 AM, Goebbe wrote: Thank you very much Jason, your help is highly appreciated! It seems that the interaction with matplotlib is a bit more complicated than what I imagined. :-) Yes, a long-term project is to overhaul the graphics code so that it exposes more of the powerful matplotlib functionality, or at least makes it easier to use matplotlib directly. Already, the .matplotlib() function goes a long ways towards that (before the matplotlib method, it was much more complicated to do things in matplotlib with Sage figures). Thanks, Jason -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: Reserved words (Sage + Cython)
Hi Dima, hi Oleksandr, On 17 Feb., 14:07, Dima Pasechnik wrote: > I imagine the behaviour is similar to Python's, where it's jolly possible > to do "list=2" and see stuff beginning to happen... But the only difference between the good and the bad version is that some function is called PC in the bad file and PCc in the good file. I guess that PC is not a reserved word. However, Oleksandr: What is one supposed to do in order to reproduce the error? When I start a sage session and attach Main.sage, then it fails with both the bad and the good version. Cheers, Simon -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: How-to change the size of ticks ? ( use of graphs for presentations )
Thank you very much Jason, your help is highly appreciated! It seems that the interaction with matplotlib is a bit more complicated than what I imagined. :-) I tried your code and it worked fine, but the xmin, xmax ... has been ignored. After experimenting I found the place, where I have to put these parameters. Here is the code: P = [1/6,1/6,1/6,1/6,1/6,1/6] X = [1,2,3,4,5,6] discrDistr = [(X[_],P[_]) for _ in range(len(P))] # Prepare values for scatter_plot p1 = scatter_plot(discrDistr, markersize=100,facecolor='blue') counter = 0 for expr in P: p1 += line([(X[counter],0), (X[counter],expr)],linestyle="--",color='black',thickness=2) counter = counter + 1 p1.axes_width(2) m=p1.matplotlib(fontsize=20,xmin=0,xmax=(len(P)+0.5),ymax=0.3 ) from matplotlib import pyplot xticks = pyplot.getp(m.axes[0], 'xticklines') #get tick parameters yticks = pyplot.getp(m.axes[0], 'yticklines') pyplot.setp(xticks, markeredgewidth=2, markersize=10) #set tick parameters pyplot.setp(yticks, markeredgewidth=2, markersize=10) from matplotlib.backends.backend_agg import FigureCanvasAgg m.set_canvas(FigureCanvasAgg(m)) m.savefig('test.png') Thanks again! Goebbe -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Fastest Lattice Reduction
I need to reduce a lattice of dimension 200 with its entries sizes are of size like 3000 bit. I use LLL(algorithm="fpLLL:fast") for faster lattice reduction. But it seems there is a problem in the function. Reduction is very bad. Is there any way to reduce this size of matrix efficiently? -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: Reserved words (Sage + Cython)
In gmane.comp.mathematics.sage.support, you wrote: > After upgrading from version 4.7.2 to 4.8, one function of dozen is stopped > working. I use a combination of Sage + Cython. You can find examples in the > attachments. > > The main problem is: when you use "PC" as the function name in "*.c" file > sage gives an error > > /home/hamsin/bin/sage/local/lib/libcsage.so(print_backtrace+0x31)[0x7f3c8b89e3a3] > /home/hamsin/bin/sage/local/lib/libcsage.so(sigdie+0x14)[0x7f3c8b89e3d5] > /home/hamsin/bin/sage/local/lib/libcsage.so(sage_signal_handler+0x20e)[0x7f3c8b89e000] > /lib/x86_64-linux-gnu/libpthread.so.0(+0x10060)[0x7f3c8dc93060] > /home/hamsin/bin/sage/local/lib/libreadline.so.6(PC+0x0)[0x7f3c861f83cc] > > > Unhandled SIGSEGV: A segmentation fault occurred in Sage. > This probably occurred because a *compiled* component of Sage has a bug > in it and is not properly wrapped with sig_on(), sig_off(). You might > want to run Sage under gdb with 'sage -gdb' to debug this. > Sage will now terminate. > > local/bin/sage-sage: line 460: 10163 Segmentation fault python "$@" > > If I use "PCc" or "PC_1", then there are no problems. So this is a bug, > feature or Cython has limitations on function names. If the last point, > then where I can see this limitations. I imagine the behaviour is similar to Python's, where it's jolly possible to do "list=2" and see stuff beginning to happen... Just in case, Dima > > Best regards, > Oleksandr -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: Modular operation in multivariate polynomials
Hi all, On 17 Feb., 10:53, Simon King wrote: > > No, I havn't. If this is not a problem for you then open. > > OK, I'll do so later today. I opened http://trac.sagemath.org/sage_trac/ticket/12529 Best regards, Simon -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Reserved words (Sage + Cython)
Hi All, After upgrading from version 4.7.2 to 4.8, one function of dozen is stopped working. I use a combination of Sage + Cython. You can find examples in the attachments. The main problem is: when you use "PC" as the function name in "*.c" file sage gives an error /home/hamsin/bin/sage/local/lib/libcsage.so(print_backtrace+0x31)[0x7f3c8b89e3a3] /home/hamsin/bin/sage/local/lib/libcsage.so(sigdie+0x14)[0x7f3c8b89e3d5] /home/hamsin/bin/sage/local/lib/libcsage.so(sage_signal_handler+0x20e)[0x7f3c8b89e000] /lib/x86_64-linux-gnu/libpthread.so.0(+0x10060)[0x7f3c8dc93060] /home/hamsin/bin/sage/local/lib/libreadline.so.6(PC+0x0)[0x7f3c861f83cc] Unhandled SIGSEGV: A segmentation fault occurred in Sage. This probably occurred because a *compiled* component of Sage has a bug in it and is not properly wrapped with sig_on(), sig_off(). You might want to run Sage under gdb with 'sage -gdb' to debug this. Sage will now terminate. local/bin/sage-sage: line 460: 10163 Segmentation fault python "$@" If I use "PCc" or "PC_1", then there are no problems. So this is a bug, feature or Cython has limitations on function names. If the last point, then where I can see this limitations. Best regards, Oleksandr Machine: linux: Linux pcen 3.0.0-16-generic #28-Ubuntu SMP Fri Jan 27 17:44:39 UTC 2012 x86_64 x86_64 x86_64 GNU/Linux sage: 'Sage Version 4.8, Release Date: 2012-01-20' -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org Cython_bad.tar.gz Description: Binary data Cython_good.tar.gz Description: Binary data
[sage-support] Re: How-to change the size of ticks ? ( use of graphs for presentations )
On 2/17/12 3:32 AM, Goebbe wrote: Hi, this is my first post. Please keep in mind that I have just started to use Sage. I use the sage notebook in order to prepare graphs for a introductory statistics class. Since I use the graphs in presentations (powerpoint) - I modified linewidth, fontsize in order to get a graph that is easily visible in the presentation (even from the back of the room). Unfortunately I did not find a way to change the size of ticks. I already searched the documentation of sage and of matplotlib, but I just did not manage to get this work. Yeah, you have to use matplotlib. I followed this message: http://www.mail-archive.com/matplotlib-users@lists.sourceforge.net/msg18998.html Here is the result: http://aleph.sagemath.org/?q=1de1fd37-f4cb-4501-a13e-84769fd5befe (click Evaluate, then look at the png file at the bottom) Here is the code: P = [1/6,1/6,1/6,1/6,1/6,1/6] X = [1,2,3,4,5,6] discrDistr = [(X[_],P[_]) for _ in range(len(P))] # Prepare values for scatter_plot p1 = scatter_plot(discrDistr, markersize=100, facecolor='blue',xmin=0,xmax=(len(P)+0.5),ymax=0.3) counter = 0 for expr in P: p1 += line([(X[counter],0),(X[counter],expr)], linestyle="--",color='black',thickness=2) counter = counter + 1 p1.axes_width(2) m=p1.matplotlib(fontsize=20) from matplotlib import pyplot xticks = pyplot.getp(m.axes[0], 'xticklines') yticks = pyplot.getp(m.axes[0], 'yticklines') # adjust markeredgewidth and markersize to adjust the width and length of tickmarks pyplot.setp(xticks, markeredgewidth=4, markersize=10) pyplot.setp(yticks, markeredgewidth=2, markersize=12) from matplotlib.backends.backend_agg import FigureCanvasAgg m.set_canvas(FigureCanvasAgg(m)) m.savefig('test.png') Thanks, Jason -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Normal Distribution
Thanks for the help. On 17 February 2012 16:00, Vegard Lima wrote: > On Fri, Feb 17, 2012 at 10:52 AM, Santanu Sarkar > wrote: >> How to generate 1000 random integers which follow normal >> distribution with mean 0 and variance 0.1? > > You can do this with numpy: > > sage: import numpy as np > sage: mu, sigma = 0, sqrt(0.1) # mean and standard deviation > sage: s = np.random.normal(mu, sigma, 1000) > > Note that it takes std.deviation as input not variance. > > > Cheers, > -- > Vegard > > -- > To post to this group, send email to sage-support@googlegroups.com > To unsubscribe from this group, send email to > sage-support+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-support > URL: http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: Normal Distribution
Not sure what generating "integers" means, when drawing from a normal, but if you just want to draw random numbers, the following should do it: NV001 = RealDistribution('gaussian',sqrt(0.1)) #N(0,0.1) mean=0 std dev = sqrt(0.1) randomdraws = [NV001.get_random_element() for _ in range(1000)] -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] How-to change the size of ticks ? ( use of graphs for presentations )
Hi, this is my first post. Please keep in mind that I have just started to use Sage. I use the sage notebook in order to prepare graphs for a introductory statistics class. Since I use the graphs in presentations (powerpoint) - I modified linewidth, fontsize in order to get a graph that is easily visible in the presentation (even from the back of the room). Unfortunately I did not find a way to change the size of ticks. I already searched the documentation of sage and of matplotlib, but I just did not manage to get this work. This is what I have currently: P = [1/6,1/6,1/6,1/6,1/6,1/6] X = [1,2,3,4,5,6] discrDistr = [(X[_],P[_]) for _ in range(len(P))] # Prepare values for scatter_plot p1 = scatter_plot(discrDistr, markersize=100, facecolor='blue',xmin=0,xmax=(len(P)+0.5),ymax=0.3) counter = 0 for expr in P: p1 += line([(X[counter],0),(X[counter],expr)], linestyle="--",color='black',thickness=2) counter = counter + 1 p1.axes_width(2) p1.show(fontsize=20) If you evaluate the code in Notebook, you will get a nice, simple graph with big fonts and larger lines. However the ticks (small lines at the axis) are too small to be visible. How can I manage to change the size/width of the ticks? Any help would be appreciated. Thanks in advance -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Normal Distribution
On Fri, Feb 17, 2012 at 10:52 AM, Santanu Sarkar wrote: > How to generate 1000 random integers which follow normal > distribution with mean 0 and variance 0.1? You can do this with numpy: sage: import numpy as np sage: mu, sigma = 0, sqrt(0.1) # mean and standard deviation sage: s = np.random.normal(mu, sigma, 1000) Note that it takes std.deviation as input not variance. Cheers, -- Vegard -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: Modular operation in multivariate polynomials
Hi Simon, I agree with you. My previous message is true only for GF(2^n). Best regards, Oleksandr -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: Modular operation in multivariate polynomials
Hi Oleksandr, On 17 Feb., 10:33, Oleksandr Kazymyrov wrote: > No, I havn't. If this is not a problem for you then open. OK, I'll do so later today. > At the moment I use the following code: > > pol=sum([g.mod(P("y^{0}+y".format(1< = GF(3)[] sage: p = P.random_element() sage: p x^2 + x*y - 1 sage: p.monomials() [x^2, x*y, 1] sage: p.coefficients() [1, 1, 2] sage: sum(p.monomials()) == p False So, you must not forget to multiply each monomial with its coefficient, for example: sage: sum([c*m for c,m in zip(p.coefficients(),p.monomials())]) == p True Best regards, Simon -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Normal Distribution
How to generate 1000 random integers which follow normal distribution with mean 0 and variance 0.1? -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: Modular operation in multivariate polynomials
Hi Simon, >> Do you have a trac account, or shall I open a trac ticket myself? No, I havn't. If this is not a problem for you then open. At the moment I use the following code: pol=sum([g.mod(P("y^{0}+y".format(1